Maurice purchased a coin collection several years ago. Each year he has had the

Question

Maurice purchased a coin collection several years ago. Each year he has had the collection appraised by a reputable coin dealer. Maurice has calculated the yearly percentage gain or loss based on the appraisal, as shown below:

Year 1: 10%

Year 2: 5%

Year 3: 9%

Year 4: -5%

Year 5: 2%

Year 6: -3%

Year 7: 12%

What is the average (mean) return of the coin collection over the seven-year period?

Use the rate of return data provided by Maurice to calculate the geometric mean return. How does this compare to the mean return?

Explanation / Answer

Average rate of return = average of all the values given = (10%+5%+...+12%)/ = 30%/7 = 4.2857%

geometric mean return = (Geometric mean of (1+r%) of all the above values) - 1

= {(1+10%)*(1+5%)*...*(1+12%)}^(1/7) - 1= 4.1057%

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